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论文题目:	Two faces of greedy leaf removal procedure on graphs
论文题目英文:
作者:	Zhao, Jin-Hua; Zhou, Hai-Jun
论文出处:
刊物名称:	JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
年:	2019
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期:
页:	83401
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摘要:	The greedy leaf removal (GLR) procedure on a graph is an iterative removal of any vertex with degree one (leaf) along with its nearest neighbor (root). Its result has two faces: a residual subgraph as a core, and a set of removed roots. While the emergence of cores on uncorrelated random graphs was solved analytically, a theory for roots is ignored except in the case of Erdos- Renyi random graphs. Here we analytically study roots on random graphs. We further show that, with a simple geometrical interpretation and a concise mean-field theory of the GLR procedure, we reproduce the zero-temperature replica symmetric estimation of relative sizes of both minimal vertex covers and maximum matchings on random graphs with or without cores.
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